Color processing apparatus, color processing method and computer readable medium

ABSTRACT

The color processing apparatus includes: a first color signal obtaining unit that obtains a first color signal in a first color space; a color conversion unit that converts the first color signal in the first color space into a second color signal in a second color space according to a color conversion characteristic associating a color signal in the first color space with a color signal in the second color space; a calculation unit that calculates a distance of the first color signal to an outer boundary of a color gamut in the first color space; and a color conversion characteristic generation unit that generates the color conversion characteristic to be used by the color conversion unit to make the conversion. The color conversion characteristic generation unit changes a generation condition of the color conversion characteristic according to the distance of the first color signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is based on and claims priority under 35 USC §119 fromJapanese Patent Application No. 2007-155598 filed Jun. 12, 2007.

BACKGROUND

1. Technical Field

The present invention relates to a color processing apparatus, a colorprocessing method and a computer readable medium storing a program.

2. Related Art

Apparatuses for inputting and outputting color images each performprocessing of outputting a color image by converting an input colorsignal, for example, in the RGB color space, into a color signal, forexample, in a device-independent L*a*b* color space, and by furtherconverting the resultant color signal into a color signal, for example,in the CMYK color space which is an output color space in the apparatus.As such apparatuses, there are, for example, an image forming apparatussuch as a printer, a display such as a liquid crystal display and animage reading apparatus such as a scanner. When performing the out-putprocessing, each of the apparatuses estimates a color conversioncharacteristic indicating a correspondence between the CMYK color spaceand the L*a*b* color space, for example, on the basis of pairs eachincluding actual data pieces actually measured in the CMYK color space,and actual data pieces actually measured in the L*a*b* color space (thispair is called an actual data pair, below). Thus, the apparatusgenerates colors that do not exist in the actual data pairs.

SUMMARY

According to an aspect of the present invention, there is provided acolor processing apparatus including: a first color signal obtainingunit that obtains a first color signal in a first color space; a colorconversion unit that converts the first color signal in the first colorspace obtained by the first color signal obtaining unit into a secondcolor signal in a second color space according to a color conversioncharacteristic associating a color signal in the first color space witha color signal in the second color space; a calculation-unit thatcalculates a distance of the first color signal to an outer boundary ofa color gamut in the first color space; and a color conversioncharacteristic generation unit that generates the color conversioncharacteristic to be used by the color conversion unit to make theconversion. The color conversion characteristic generation unit changesa generation condition of the color conversion characteristic accordingto the distance of the first color signal calculated by the calculationunit.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiment (s) of the present invention will be described indetail based on the following figures, wherein:

FIG. 1 is a block diagram showing an entire configuration of a colorprocessing apparatus to which the first exemplary embodiment is applied;

FIG. 2 is a diagram for explaining the outer boundaries of the colorgamut in the L*a*b* color space;

FIG. 3 is a diagram showing a color conversion characteristic in a casewhere actual data pairs are weighted for the first color signal (x_(1j),x_(2j), x_(3j), x_(4j)) around the outer boundary of the color gamut inthe same manner as that for the first color signal far from the outerboundary of the color gamut;

FIG. 4 is a diagram for explaining the weight determined by the firstfunction and the second function generated by the weight data generatorof the first exemplary embodiment;

FIG. 5 is a diagram for schematically explaining a relation between thewidth of the weight and the color difference distance of the first colorsignal to the outer boundary of the color gamut;

FIG. 6 is a diagram for explaining weight determined by a first functionand a second function for a case where second color signals in the CMYKcolor spaces as output signals, are estimated from first color signalsin the L*a*b* color space, as input signals;

FIG. 7 is a diagram for explaining the color difference distance in theL*a*b* color space;

FIG. 8 is a diagram showing a configuration in which the color-gamutdistance calculator figures out the color difference distance by use ofthe second color signal calculated by the color conversion unit;

FIG. 9 is a diagram for explaining the weight determined by a firstfunction and a second function generated by a weight data generator ofthe second exemplary embodiment;

FIG. 10 is a diagram for schematically explaining a relation between theshift amount of the center of the weight and the color differencedistance from an input signal (first color signal) to the outer boundaryof the color gamut; and

FIG. 11 is a diagram for explaining the weight determined by the firstfunction and the second function of Equations 15 and 16 in a case wheresecond color signals in the CMYK color space as output signals areestimated from first color signals in the L*a*b* color space as inputsignals.

DETAILED DESCRIPTION

Hereinbelow, detailed descriptions for exemplary embodiments of thepresent invention will be given with reference to the accompanyingdrawings.

First Exemplary Embodiment

FIG. 1 is a block diagram showing an entire configuration of a colorprocessing apparatus 1 to which the first exemplary embodiment isapplied. The color processing apparatus 1 in FIG. 1 includes an imagedata input unit 10, a color conversion characteristic generation unit20, a color conversion unit 30 and an image data output unit 40.

Note that, in the color processing apparatus 1, a CPU (centralprocessing unit) (not shown in the figure) reads, from a main memory(not shown) to a RAM (random access memory) or the like in the colorprocessing apparatus 1, programs implementing functions of the imagedata input unit 10, the color conversion characteristic generation unit20, the color conversion unit 30 and the image data output unit 40, andthen performs various kinds of processing.

The image data input unit 10 is an example of a first color signalobtaining unit, and is a functional unit to which a color signal ofimage data, or a color signal representing each lattice point in a colorconversion table is inputted. More specifically, as the color signal ofimage data, or as the color signal representing the lattice point in thecolor conversion table, the image data input unit 10 obtains colorsignals (first color signals), for example, in the CMYK color space thatare to be processed in a color image forming apparatus or the like suchas a color printer, and is dependent of its device (device-dependentcolor spaced). Thereafter, the image data input unit 10 outputs theobtained first color signals to the color conversion characteristicgeneration unit 20 and to the color conversion unit 30.

The color conversion characteristic generation unit 20 is a functionalunit, as will be described later, that generates a color conversioncharacteristic used at the time of color conversion processing in thecolor conversion unit 30.

The color conversion unit 30 is a functional unit that performs colorconversion processing according to the color conversion characteristicgenerated by the color conversion characteristic generation unit 20. Inother words, according to the color conversion characteristic, the colorconversion unit 30 converts the first color signals, for example, in theCMYK color space obtained from the image data input unit 10, into colorsignals (second color signals), for example, in the L*a*b* color spacethat is a color space independent of the device (device-independentcolor space) Thereafter, the color conversion unit 30 outputs, to theimage data output unit 40, the image data expressed as the second colorsignals obtained by the conversion.

The image data output unit 40 is a functional unit that outputs theimage data to the outside of the color processing apparatus 1. In otherwords, the image data output unit 40 outputs the image data expressed asthe second color signals resulting from the color conversion processingby the color conversion unit 30, to a, functional unit or the like (notshown) that performs processing of converting the image data into dataexpressed within a color gamut of a color image forming apparatus or thelike, for example. A general color image forming apparatus or the likeperforms processing called a gamut mapping algorithm (GMA) forcompressing the color gamut of inputted data into the color gamutspecific to the color image forming apparatus. The image data outputunit 40 outputs, to such a functional unit or the like that performs theGMA, the image data expressed as the second color signals.

It should be noted that, in the present description, a color signal thatis inputted from the image data input unit 10 but not converted yet bythe color conversion unit 30 is defined as the “first color signal.”Meanwhile, a color signal that is outputted to the image data outputunit 40 and is already converted by the color conversion unit 30 isdefined as the “second color signal.”

Next, an explanation will be given for the color conversioncharacteristic generation unit 20.

The color conversion characteristic generation unit 20 includes acolor-gamut distance calculator 21, an actual data pair memory 22, and aweight data generator 23.

The color-gamut distance calculator 21 is an example of a calculationunit, and calculates a distance d of a first color signal to an outerboundary of a color gamut (color difference distance) For example, in acase where a first color signal in the CMYK color space is convertedinto a second color signal in the L*a*b* color space, outer boundariesof the color gamut in the L*a*b* color space are formed as shown in FIG.2 (a diagram for explaining the outer boundaries of the color gamut inthe L*a*b* color space) There are three patterns, shown below, of colorcoordinates (C, M, Y, K) in the CMYK color space corresponding to theouter boundaries of the color gamut in the L*a*b* color space shown inFIG.

To be precise, since color coordinates (C, M, Y, K) of the CMYK colorspace are generally expressed as color-coordinate values of C, M, Y, K=0to 100, the color coordinates (C, M, Y, K) in accordance with any one ofthe following three patterns correspond to a coordinate point on one ofthe outer boundaries of the color gamut of the L*a*b* color space:

(1) K=0, and any one of C, M and Y is 0;

(2) any one of C, M and Y is 0, and any one of C, M and Y is 100; and

(3) K=100, and any one of C, M and Y is 100.

Accordingly, the color difference distance d of the first color signalto the outer boundary of the color gamut may be calculated as theshortest one of the distances between the first color signal and theabove-mentioned coordinate points (1) to (3)

Specifically, the color difference distance d of the first color signalto the outer boundary of the color gamut may be figured out as theshortest one of four dimensional Euclidean distances between the firstcolor signal and the above-mentioned coordinate points (1) to (3) byusing one of the following ways, for example.

(A) In a case where K≠(not equal) 0 and K≠ (not equal) 100, the maximumvalue component and the minimum value component of the color componentsof the first color signal (C, M, Y, K) are extracted. Then, if themaximum value component is K, a color component having the next largestvalue or having the same value as tale maximum value component K isextracted. Since K is the maximum value component in this case, theminimum four-dimensional Euclidean distance to the first color signal(C, M, Y, K) is given by the outer boundary of the color gamut havingK=100 and having the color component of the next largest value or thesame value as the maximum value component K (any one of C, M and Y)=100.Specifically, in this case, the color difference distance d to the outerboundary of the color gamut is the four-dimensional Euclidean distancebetween the first color signal (C, M, Y, K) and any one of the colorcoordinate points such as (100, M, Y, 100), (C100, Y, 100) and (C, M,100, 100) on the outer boundaries of the color gamut of theabove-mentioned (3).

(B) In a case where K≠(not equal) 0 and K≠(not equal) 100, the maximumvalue component and the minimum value component of the color componentsof the first color signal (C, M, Y, K) are extracted. Then, if theminimum value component is K, a color component having the next smallestvalue or having the same value as the minimum value component K isextracted. Since K is the minimum value component in this case, theminimum four-dimensional Euclidean distance to the first color signal(C, M, Y, K) is given by the outer boundary of the color gamut havingK=0 and having the color component of the next smallest value or thesame value as the minimum value component K (any one of C, M and Y)=0.Specifically, in this case, the color difference distance d to the outerboundary of the color gamut is the four-dimensional Euclidean distancebetween the first color signal (C, M, Y, K) and any one of the colorcoordinate points such as (0, M, Y, 0), (C, 0, Y, 0) and (C, M, 0, 0) onthe outer boundaries of the color gamut of the above-mentioned (1).

(C) In a case where K≠(not equal) 0 and K≠(not equal), 100, the maximumvalue component and the minimum value component of the color componentsof the first color signal (C, M, Y, K) are extracted. Then, if neitherof the maximum value component nor the minimum value component is K, theminimum four-dimensional Euclidean distance to the first color signal(C, M, Y, K) is given by the outer boundary of the color gamut havingthe color component of the maximum value component (any one of C, M, andY)=100 and the color component of the minimum value component (any oneof C, M and Y)=0. Specifically, in this case, the color differencedistance d to the outer boundary of the color gamut is thefour-dimensional Euclidean distance between the first color signal (C,M, Y, K) and any one of the color coordinate points such as (0, 100, Y,K), (0, M, 100, K), (100, 0, Y, K), (100, M, 0, K), and the like on th,eouter boundary of the color gamut of the above-mentioned (2).

(D) In a case where K=0, the minimum value component of the C, M, and Ycolor components of the first color signal (C, M, Y, K) are extracted.In this case, the minimum four-dimensional Euclidean distance to thefirst color signal (C, M, Y, K) is given by the outer boundary of thecolor gamut having the color component having the minimum valuecomponent (any one of C, M and Y)=0. Specifically, the color differencedistance d to the outer boundary of the color gamut is thefour-dimensional Euclidean distance between the first color signal (C,M, Y, K) and any one of the color coordinate points such as (0, M, Y,0), (C, 0, Y, 0) and (C, M, 0, 0) on the outer boundaries of the colorgamut of the above-mentioned (1).

(E) In a case where K=100 the maximum value component of the C, M, and Ycolor components of the first color signal (C, M, Y, K) are extracted.In this case, the minimum four-dimensional Euclidean distance to thefirst color signal (C, M, Y, K) is given by the outer boundary of thecolor gamut having the color component having the maximum valuecomponent (any one of C, M and Y)=100. Specifically, the colordifference distance d to the outer boundary of the color gamut is thefour-dimensional Euclidean distance between the first color signal (C,M, Y, K) and any one of the color coordinate points such as (100, M, Y,100), (C, 100, Y, 100) and (C, M, 100, 100) on the outer boundaries ofthe color gamut of the above-mentioned (3).

Here, an exemplar calculation is given for a color difference distance dof a first color signal to an outer boundary of a gamut. For example, ina case where the first color signal is (C, M, Y, K)=(90, 95, 80, 100),the above (E) is applicable, and the color difference distance d to theouter boundary of the color gamut is the four-dimensional Euclideandistance to a color coordinate point on the above-mentioned outerboundary of the color gamut (3). More precisely, since the maximum valuecomponent of the color components C, M, and Y is 95 of the component M,the color difference distance d is calculated as the distance betweenthe first color signal (90, 95, 800, 100) and the color coordinate point(90, 100, 80, 100) having the component M set to 100 on the outerboundary of the color gamut. Namely, the following Equation 1 gives thecolor difference distance d to the outer boundary of the color gamut

$\begin{matrix}\begin{matrix}{d = \sqrt{\left( {90 - 90} \right)^{2} + \left( {100 - 95} \right)^{2} + \left( {80 - 80} \right)^{2} + \left( {100 - 100} \right)^{2}}} \\{= \sqrt{5^{2}}} \\{= 5}\end{matrix} & (1)\end{matrix}$

Further, for example, in a case where the first color signal is (C, M,Y, K)=(100, 5, 80, 20), the above (C) is applicable, and the colordifference distance d to the outer boundary of the color gamut is thefour-dimensional Euclidean distance to a color coordinate point on theabove-mentioned outer boundary of the color gamut (2). More precisely,since the maximum value component of the color components C, M, and Y is100 of the component C and the minimum value component of the colorcomponents C, M, and Y is 5 of the component M, the color differencedistance d is calculated as the distance between the first color signal(100, 5, 80, 20) and the color coordinate point (100, 0, 80, 20) havingthe component M set to 0 on the outer boundary of the color gamut.Namely, the following Equation 2 gives the color difference distance dto the outer boundary of the color gamut.

$\begin{matrix}\begin{matrix}{d = \sqrt{\left( {100 - 100} \right)^{2} + \left( {5 - 0} \right)^{2} + \left( {80 - 80} \right)^{2} + \left( {20 - 20} \right)^{2}}} \\{= \sqrt{5^{2}}} \\{= 5}\end{matrix} & (2)\end{matrix}$

Furthermore, for example, in a case where the first color signal is (C,M, Y, K)=(95, 20, 80, 95), the above (A) is applicable, and the colordifference distance d to the outer boundary of the color gamut is thefour-dimensional Euclidean distance to a color coordinate point on theabove-mentioned outer boundary of the color gamut (3). More precisely,since the maximum value component is K and a color component having thenext largest value or having the same value as the maximum valuecomponent K is 95 of the component C, the color difference distance d iscalculated as the distance between the first color signal (95, 20, 80,95) and the color coordinate point (100, 20, 80, 100) having thecomponents K and C set to 100 on the outer boundary of the color gamut.Namely, the following Equation 3 gives the color difference distance dto the outer boundary of the color gamut.

$\begin{matrix}\begin{matrix}{d = \sqrt{\left( {100 - 95} \right)^{2} + \left( {20 - 20} \right)^{2} + \left( {80 - 80} \right)^{2} + \left( {100 - 95} \right)^{2}}} \\{= \sqrt{5^{2} + 5^{2}}} \\{= \sqrt{50}}\end{matrix} & (3)\end{matrix}$

Note that the calculation method for the color difference distance d ofthe first color signal to the outer boundary of the color gamut is notlimited to the above method, and that any method may be employed, aslong as the method is one that calculates the distance of the firstcolor signal to the outer boundary of the color gamut.

Incidentally, in a case where the first color signal represents colorcoordinates (R, G, B) in the RGB color pace, the coordinates aregenerally expressed as coordinate values of R, G, B=0 to 255. For thisreason, in this case, color coordinates (R, G, B) in which any one of R,G, and B is equal to 0 or 255 correspond to a coordinate point on theouter boundary of the color gamut in the L*a*b* color space.

Subsequently, the actual data pair memory 22 stores therein multipleactual data pairs each composed of actual data sets in two differentcolor spaces corresponding to each other. Here, the different colorspaces are targeted for a color conversion characteristic estimationthat is to be actually performed in the color conversion unit 30. To bespecifics the actual data pair memory 22 stores n actual data sets(x_(1i), x_(2i), x_(3i), x_(4i)) expressed in the CMYK color space, forexample, which are input signals (first color signals) and n actual datasets (y_(1i), y_(2i), y_(3i)) expressed in the L*a*b* color space, forexample, which are output signals (second color signals) correspondingto the input signals. Here, n and i each are an integer, and i=1 to n(the same is applied below).

In the case of a color image forming apparatus, for example, variouscombinations of color signals (C, M, Y, K) in the CMYK color space areprocessed and printed to make color patches (color samples), and thenthe color of each of the color patches is measured (color measuring) ascoordinates in the L*a*b* color space, for example. Hence, prepared isan actual data pair of an actual data set representing the input signal(C, M, Y, K) for each color patch, and an actual data set representingthe color coordinates (L*, a*, b*) in the L*a*b* color space obtained bymeasuring the color patch that is the output image. Then, the actualdata pair memory 22 stores therein the actual data pairs each consistingof the actual data set of the input signal (C, M, Y, K) and the actualdata set of the color coordinates (L*, a*, b*) of the output imagecorresponding to the input signal.

The weight data generator 23 is an example of a color conversioncharacteristic generation unit that obtains the actual data pairs fromthe actual data pair memory 22, and controls weight (weighting) of theactual data pairs for estimating the color conversion characteristic inthe color conversion unit 30. Here, the weight is controlled accordingto the color difference distance d, calculated in the color-gamutdistance calculator 21, of the first color signal (input signal) to theouter boundary of the color gamut.

Here, first of all, an explanation will be given for an estimation of acolor conversion characteristic made in the color processing apparatus 1according to the first exemplary embodiment. The color processingapparatus 1 estimates a color conversion characteristic specific to acolor image forming apparatus, for example, and generates, according tothe estimated color conversion characteristic, a second color signalfrom an inputted first color signal. In other words, the colorprocessing apparatus 1 estimates the color conversion characteristicindicating a correspondence between a color signal (C, M, Y, K) in theCMYK color space and color coordinates (L*, a*, b*) in the L*a*b* colorspace by use of the above-mentioned actual data pairs. Then, accordingto these color conversion characteristic, the color processing apparatus1 generates colors which are not included in the actual data pair.

The following shows an exemplar case of estimating a color conversioncharacteristic indicating a correspondence of a color signal (C, M, Y,K) in the four-dimensional CMYK color space as a first color signal,with a color signal (L*, a*, b*) in the three-dimensional L*a*b* colorspace as a second color signal. It should be noted that the followingcase is similarly applicable to the case of estimating a colorconversion characteristic indicating a correspondence of a color signal(R, G, B) in the three-dimensional RGB color space, for example, withcolor coordinates (L*, a*, b*) in the three-dimensional L*a*b* colorspace, for example.

In a case where the first color signal is of four-dimensional data ofthe CMYK color space, and the second color signal is ofthree-dimensional data of the La*b* color space, the color processingapparatus 1 associates n actual data sets (x_(1i), x_(2i), x_(3i),x_(4i)) of the first color signals with output estimation values thereof(y′_(1i), y′_(2i), y′_(3i)) by use of a matrix having components of m₁₁,m₁₂, m₁₃, m₁₄, . . . , so as to form a linear relation including aconstant term, as shown in Equation 4 below.

$\begin{matrix}{\begin{pmatrix}y_{1i}^{\prime} \\y_{2i}^{\prime} \\y_{3i}^{\prime}\end{pmatrix} = {\begin{pmatrix}m_{11} & m_{12} & m_{13} & m_{14} & m_{15} \\m_{21} & m_{22} & m_{23} & m_{24} & m_{25} \\m_{31} & m_{32} & m_{33} & m_{34} & m_{35}\end{pmatrix}\left( \begin{matrix}x_{1i} \\x_{2i} \\x_{3i} \\x_{4i} \\1\end{matrix}\; \right)}} & (3)\end{matrix}$

Then, by use of the following Equation 5, obtained is a sum of squaresE_(j) of weighted Euclidean distances between the output estimationvalues (y′_(1i), y′_(2i), y′_(3i)) obtained from the actual data sets(x_(1i), x_(2i), x_(3i), x_(4i)) of the first color signals by use ofthe matrix in Equation 4, and the actual data sets (y_(1i), y_(2i),y_(3i)) of the second color signals corresponding to the actual datasets (x_(1i), x_(2i), x_(3i), x_(4i)) of the first color signals.

Here, W_(ij), denotes a weighting coefficient (also referred to as“weight” below) for the Euclidean distance between the output estimationvalues (y′_(1i), y′_(2i), y′_(3i)) obtained from the actual data set(x_(1i), x_(2i), x_(3i), x_(4i)) of the first color signal by use of thematrix in equation 4, and the actual data set (y_(1i), y_(2i), y_(3i))of the second color signal.

$\begin{matrix}{E_{j} = {\sum\limits_{i = 0}^{n}\left( {W_{ij}^{2}\left( {\left( {y_{1i}^{\prime} - y_{1i}} \right)^{2} + \left( {y_{2i}^{\prime} - y_{2i}} \right)^{2} + \left( {y_{3i}^{\prime} - y_{3i}} \right)^{2}} \right)} \right)}} & (5)\end{matrix}$

Meanwhile, by use of the following equation 6, the second color signal(y_(1j), y_(2j), y_(3j)) that is estimated values is obtained from thefirst color signal (x_(1j), x_(2j), x_(3j), x_(4j)) that is values basedon which the estimation is made (such values are called estimation-basevalues, below). The matrix in Equation 6 is the same as that in Equation4. If the estimation-base values are the first color signal (x_(1j),x_(2j), x_(3j), x_(4j)), the estimated values of the second color signal(y_(1j), y_(2i), y_(3i)) are obtained by substituting estimation-basevalues into Equation 6.

$\begin{matrix}{\begin{pmatrix}y_{1j} \\y_{2j} \\y_{3j}\end{pmatrix} = {\begin{pmatrix}m_{11} & m_{12} & m_{13} & m_{14} & m_{15} \\m_{21} & m_{22} & m_{23} & m_{24} & m_{25} \\m_{31} & m_{32} & m_{33} & m_{34} & m_{35}\end{pmatrix}\begin{pmatrix}x_{1j} \\x_{2j} \\x_{3j} \\x_{4j} \\1\end{pmatrix}}} & (6)\end{matrix}$

Subsequently, by use of a known method termed as the least squaremethod, each of matrix components m₁₁, m₁₂, m₁₃, m₁₄, . . . , isobtained under the condition of minimizing E_(j) where the weight W_(ij)is fixed. In the case where the weight W_(ij) depends on the matrixcomponents or the second color signal that is the estimated values, eachof the matrix components m₁₁, m₁₂, m₁₃, m₁₄, . . . , cannot be uniquelydetermined. Accordingly, in this case, under the condition of minimizingE_(j) in Equation 5, the weight W_(ij), each of the matrix componentsm₁₁, m₁₂, m₁₃, m₁₄, . . . , and the optimal values of estimated valuesare determined by use of the iteration method.

Note that, in the color processing apparatus 1 of the first exemplaryembodiment, the matrix in Equation 6 thus obtained is set in the colorconversion unit 30. Then, the color conversion unit 30 calculates thesecond color signal (y_(1j), y_(2j), y_(3j)) that is the estimatedvalues, from the first color signal (x_(1j), x_(2j), x_(3j), x_(4j))that is the estimation-base values based on Equation 6.

The weight W_(ij) of the first exemplary embodiment is composed of afirst function F_(ij) and a second function G_(ij), each of which is amonotonically decreasing function.

The first function F_(ij) is used to normalize a difference between eachpair of corresponding signal components of the first color signal(x_(1j), x_(2j), x_(3j), x_(4j)) of the estimation-base values, and ofthe actual data set (x_(1i), x_(2i), x_(3i), x_(4i)) of the first colorsignal. Then, the first function F_(ij) defines weight W_(ij) thatmonotonously decreases according to the Euclidean distance to thenormalized signal composed of these normalized difference components.

In addition, the second function G_(ij) is used to convert a differencebetween each pair of corresponding signal components of theestimation-base values (x_(1j), x_(2j), x_(3j), x_(4j)) of the firstcolor signal and of the actual data set (x_(1i), x_(2i), x_(3i), x_(4i))of the first color signal, into a difference component havingsensitivity taken into consideration by use of each matrix component inEquations 4 and 6. Then, these difference components are normalized.After that, the second function G_(ij) defines weight W_(ij) thatmonotonously decreases according to the Euclidean distance to thenormalized signal composed of the difference components having thesensitivity taken into consideration.

In this way, the weight W_(ij) are defined by use of the twomonotonously decreasing functions depending on the Euclidean distance,that is, the first function F_(ij) and the second function G_(ij).Thereby, an actual data pair having a large difference in distance(color difference) in the color space is made less influential by makingthe weight W_(ij) smaller, while an actual data pair having a smallcolor difference is treated as important data by making the weightW_(ij) larger. In addition, since the first function F_(ij) and thesecond function G_(ij) are the monotonously decreasing function, thecontinuity of the estimated values is secured in principle, and acoefficient for color processing, for example, in a color image formingapparatus is determined without considering local discontinuities.

Here, a specific example will be described for calculating the estimatedvalues from the estimation-base values by using Equations 7 to 9, whichare shown below. In this specific example, the three-dimensional secondcolor signal (y_(1j), y_(2j), y_(3j)) of the estimated values isestimated based on the four-dimensional first color signal (x_(1j),x_(2j), x_(3j), x_(4j)) of the estimation-base values.

$\begin{matrix}{W_{1{ij}} = {F_{ij}\left( {\left( {\left( {x_{1i} - x_{1j}} \right)/x_{10}} \right)^{2} + \left( {\left( {x_{2i} - x_{2j}} \right)/x_{20}} \right)^{2} + \left( {\left( {x_{3i} - x_{3j}} \right)/x_{30}} \right)^{2} + \left( {\left( {x_{4i} - x_{4j}} \right)/x_{40}} \right)^{2}} \right)}} & (7) \\{W_{2{ij}} = {G_{ij}\left( {{\left( {\left( {m_{11}\left( {x_{1i} - x_{1j}} \right)} \right)^{2} + \left( {m_{12}\left( {x_{2i} - x_{2j}} \right)} \right)^{2} + \left( {m_{13}\left( {x_{3i} - x_{3j}} \right)} \right) + \left( {m_{14}\left( {x_{4i} - x_{4j}} \right)} \right)^{2}} \right)/\left( y_{i\; 0} \right)^{2}} + {\left( {\left( {m_{21}\left( {x_{1i} - x_{1j}} \right)} \right)^{2} + \left( {m_{22}\left( {x_{2i} - x_{2j}} \right)} \right)^{2} + \left( {m_{23}\left( {x_{3i} - x_{3j}} \right)} \right)^{2} + \left( {m_{24}\left( {x_{4i} - x_{4j}} \right)} \right)^{2}} \right)/\left( y_{20} \right)^{2}} + {\left( {\left( {m_{31}\left( {x_{1i} - x_{1j}} \right)} \right)^{2} + \left( {m_{32}\left( {x_{2i} - x_{2j}} \right)} \right)^{2} + \left( {m_{33}\left( {x_{3i} - x_{3j}} \right)} \right)^{2} + \left( {m_{34}\left( {x_{4i} - x_{4j}} \right)} \right)^{2}} \right)/\left( y_{30} \right)^{2}}} \right)}} & (8)\end{matrix}$W _(12ij) =H(W _(1ij) , W _(2ij))   (9)

Firstly, Equation 7 shows that first weight W_(1ij) is set by use of thefirst function F_(ij) that is the monotonously decreasing function ofthe normalized signal with respect to the Euclidean distance. Here, thenormalized signal is obtained by normalizing each difference componentof the first color signal, that is, a difference between each pair ofcorresponding signal components of the first color signal (x_(1j),x_(2j), x_(3j), x_(4j)) of the estimation-base values and the actualdata set (x_(1i), x_(2i), x_(3i), x_(4i)) of the first color signal.

In Equation 7, firstly obtained are the differences (x_(1i)−x_(1j)),(x_(2i)−x_(2j)), (x_(3i)−x_(3j)), (x_(4i)−x_(4j)) between all the pairsof signal components of the first color signal (x_(1j), x_(2j), x_(3j),x_(4j)) and the actual data (x_(1i), x_(2i), x_(3i), x_(4i)).Thereafter, The differences (x_(1i)−x_(1j)), (x_(2i)−x_(2j)),(x_(3i)−x_(3j)), (x_(4i)−x_(4j)) are normalized by use of constants fornormalization (x₁₀, x₂₀, x₃₀, x₄₀), thereby obtaining(x_(1i)−x_(1j))/x₁₀, (x_(2i)−x_(2j))/x₂₀, (x_(3i)−x_(3j))/x₃₀,(x_(4i)−x_(4j))/x₄₀. Then, the first weight W_(1ij) is set by using, asa parameter of the first function F_(ij), a sum of squares of thesenormalized differences.

Next, Equation 8 shows that second weight W_(2ij) is set by use of thesecond function G_(ij) that is the monotonously decreasing function ofanother normalized signal with respect to the Euclidean distance. Here,the normalized signal is obtained by firstly converting differencesbetween all the pairs of signal components of the first color signal(x_(1j), x_(2j), x_(3j), x_(4j)) of the estimation-base values and theactual data set (x_(1i), x_(2i), x_(3i), x_(4i)) of the first colorsignal are firstly converted into the difference components having thesensitivity taken into consideration by use of the respective matrixcomponent in Equations 4 and 6, and then by normalizing the resultantdifference components. Here, the conversion into the differencecomponents having the sensitivity taken into consideration is defined asa calculation in which: differences between each pair of signalcomponents of the first color signal (x_(1j), x_(2j), x_(3j), x_(4j))and the actual data set (x_(1i), x_(2i), x_(3i), x_(4i)) is multipliedby a corresponding one of the matrix components; the resultant value ofeach signal component is squared; and then the total sum of theresultant values of all the signal components is calculated. Here, thesecond function G_(ij) is configured not to depend on a plus or minussign of each signal component by calculating the squared value of eachterm, and to take the sensitivity of each term into consideration by useof the absolute value of the term.

In Equation 8, firstly, obtained are differences (x_(1i)−x_(1j)),(x_(2i)−x_(2j)), (x_(3i)−x_(3j)), (x_(4i)−x_(4j)) between all the signalcomponents of the first color signal (x_(1j), x_(2j), x_(3j), x_(4j)) ofthe estimation-base values and the actual data set (x_(1i), x_(2i),x_(3i), x_(4i)) of the first color signal. Although the differences maybe converted into the signal components In the output space bymultiplying these differences by corresponding matrix components, thecalculation here is to firstly multiply each of the differences by acorresponding one of the matrix components, to multiply each of theresultant differences by itself, and then to sum up the resultantvalues. More precisely, firstly calculated are(m₁₁(x_(1i)−x_(1j)))²+(m₁₂(x_(2i)−x_(2j)))²+(m₁₃(x_(3i)−x_(3j)))²+(m₁₄(x_(4i)−x_(4j)))²,(m₂₁(x_(1i)−x_(1j)))²+(m₂₂(x_(2i)−x_(2j)))²+(m₂₃(x_(3i)−x_(3j)))²+(m₂₄(x_(4i)−x_(4j)))²and(m₃₁(x_(1i)−x_(1j)))²+(m₃₂(x_(2i)−x_(2j)))²+(m₃₃(x_(3i)−x_(3j)))²+(m₃₄(x_(4i)−x_(4j)))².Then, by use of constants for normalization (y₁₀, y₂₀, y₃₀) these arerespectively divided by (y₁₀)², (y₂₀)², (y₃₀)², thereby beingnormalized. Thereafter, the normalized values are summed up, and areused as the parameter for the second function G_(ij) that is themonotonously decreasing function. In this way, the second weight W_(2ij)is determined.

The following Equation 9 shows that a weighting coefficient (weight)W_(ij) set by combining the forgoing two monotonously decreasingfunctions, that is, the first function F_(ij) and the second functionG_(ij). Here, these two functions are combined so as not to lose thecharacteristics that the two functions, first, function F_(ij) andsecond function G_(ij), are the monotonously decreasing functionsdepending on the Euclidean distance. For example, a mathematic operationsuch as addition or multiplication is used.

The W_(12ij) obtained with Equation 9 is the weight W_(ij) in Equation5. Then, by use of this weight W_(ij), the matrix components m₁₁, m₁₂,m₁₃, m₁₄, . . . are figured out in the least square method, so as tominimize E_(j) shown in Equation 5. The color conversion characteristicgeneration unit 20 generates such matrix components m₁₁, m₁₂, m₁₃, m₁₄,

Then, the color conversion characteristic generation unit 20 sets thematrix composed of the generated components m₁₁, m₁₂, m₁₃, m₁₄, . . . inthe color conversion unit 30. The color conversion unit 30 calculatesthe estimated values with Equation 6 using the set matrix. The colorconversion unit 30 also transmits the estimated values thus calculatedto the color conversion characteristic generation unit 20, if needed.The color conversion characteristic generation unit 20 again calculatesthe weight W_(ij) by using the estimated values calculated by the colorconversion unit 30, then obtains a matrix composed of components m₁₁,m₁₂, m₁₃, m₁₄, . . . that minimize E_(j), and finally again sets theobtained matrix in the color conversion unit 30. The color conversionunit 30 again calculates the estimated values by use of thenewly-obtained matrix. The color processing apparatus 1 repeats thisprocessing to converge each of the estimated values, and consequentlyobtains desirable estimated values.

Here, the descriptions are returned to the weight data generator 23. Asdescribed above, the weight data generator 23 obtains the actual datapair of ((x_(1i), x_(2i), x_(3i), x_(4i)), (y_(1i), y_(2i), y_(3i)))from the actual data pair memory 22. From the color-gamut distancecalculator 21, the weight data generator 23 obtains the color differencedistance d of the first color signal to the outer boundary of the colorgamut. Then, according to the color difference distance d of the firstcolor signal to the outer boundary of the color gamut, the weight datagenerator 23 controls weight (weighting) to be assigned to the actualdata pair when the color conversion unit 30 estimates the colorconversion characteristic.

Equation 6 is used to estimates the color conversion characteristic bythe color conversion unit 30. By using the first function F_(ij) and thesecond function G_(ij) that are the monotonously decreasing functions,as shown in Equations 5, 7 and 8, the matrix of Equation 6 is generatedso that smaller weight would be given to actual data pairs each having alarger distance difference (color difference) to the first color signal(x_(1j), x^(2j), x_(3j), x_(4j)), which includes the estimation-basevalues, in the color space, while larger weight would be given to actualdata pairs each having a smaller color difference in the color space.With this weight, a local linear regression analysis is performed aroundthe first color signal x_(1j), x_(2j), x_(3j), x_(4j)), and consequentlythe color conversion characteristic is estimated.

On the other hand, since there is no actual data pair outside the outerboundary of the color gamut, the presence and absence of actual datapairs change drastically around the outer boundary of the color gamut.For this reason, if actual data pairs are weighed for the first colorsignal (x_(1j), x_(2j), x_(3j), x_(4j)) around the outer boundary of thecolor gamut in the same manner as that for the first color signal farfrom the outer boundary of the color gamut, the accuracy for estimatingthe color conversion for the first color signal x_(1j), x_(2j), x_(3j),x_(4j)) around the outer boundary of the color gamut is reduced.

For example, FIG. 3 is a diagram showing a color conversioncharacteristic in a case where actual data pairs are weighted for thefirst color signal (x_(1j), x_(2j), x_(3j), x_(4j)) around the outerboundary of the color gamut in the same manner as that for the firstcolor signal far from the outer boundary of the color gamut. In FIG. 3,the horizontal axis indicates color coordinates in the CMYK color spacefor the first color signal, and the vertical axis indicates colorcoordinates in the L*a*b* color space for the second color signal. Thesame axes are also used in FIGS. 4, 6, 9 and 11.

As shown in FIG. 3, around the outer boundary of the color gamut, onlythe actual data pairs inside the outer boundary of the color gamut areweighted. As a result, the calculated estimated values are lower thanthe real values of the color conversion characteristic.

More precisely, the weight W_(ij) in Equation 5 is set, with the centerthereof taken as the first color signal (x_(1j), x_(2j), x_(3j),x_(4j)), by use of the first function F_(ij) and the second functionG_(ij) that are the monotonously decreasing functions depending on theEuclidean distance of the first color signal (x_(1j), x_(2j), x_(3j),x_(4j)) to the actual data sets (x_(1i), x_(2i), x_(3i), x_(4i)) of thefirst color signal. Then, the sum of squares E_(j) in Equation 5 iscalculated by use of such weight W_(ij). Around the outer boundary ofthe color gamut outside which no actual data pair exists, however, nosquare-sum component outside the outer boundary of the color gamut isadded to the sum of squares E_(j).

For example, as shown in FIG. 3, for a certain first color signallocated far from the outer boundary of the color gamut (called theinside of the color gamut), the sum of squares E_(j) in Equation 5 iscalculated by assigning the weight W_(ij) to the actual data sets(x_(1i), x_(2i), x_(3i), x_(4i)) located on both sides of the firstcolor signal (x_(1j), x_(2j), x_(3j), x_(4j)), that is, the sides havinglarger color values and having smaller color values. On the other hand,as for a first color signal located around the outer boundary of thecolor gamut, no actual data pair exists outside the outer boundary ofthe color gamut. Accordingly, the sum of squares E_(j) in Equation 5 iscalculated only by assigning the weight W_(ij) to the actual data sets(x_(1i), x_(2i), x_(3i), x_(4i)) located on a side of the first colorsignal (x_(1j), x_(2j), x_(3j), x_(4j)), that is, the side havingsmaller color values (the shaded area in FIG. 3). Thus, a local linerregression analysis for the first color signal located around the outerboundary of the color gamut is performed with the sum of squares E_(j)to which no square-sum component outside the outer boundary of the colorgamut is added. As a result, the calculated estimated values (theestimated point shown in FIG. 3) are smaller than the values of the realcolor conversion characteristic.

For this reason, the weight data generator 23 of the first exemplaryembodiment controls the weight (weighting) to be assigned to the actualdata pairs when the color conversion characteristic is estimated by thecolor conversion unit 30 according to the color difference distance dbetween the first color signal and the outer boundary of the color gamutthat is obtained by the color-gamut distance calculator 21.

More precisely, the weight data generator 23 of the first exemplaryembodiment generates the first function F_(ij) and the second functionG_(ij) to assign the weight W_(ij) within a predetermined range of thecolor difference distance d so that the weight W_(ij) would be assignedto actual data sets in a wider area as the color difference distance dis smaller. Here, the color difference distance d is a distance betweenthe first color signal and the outer boundary of the color gamut, and isobtained from the color-gamut distance calculator 21.

In other words, the weight data generator 23 generates the firstfunction F_(ij) and the second function G_(ij) such that, the smallerthe color difference distance d is, the wider the area including actualdata pairs to be assigned the weight W_(ij) would be.

Then, the weight data generator 23 calculates the weight W_(12ij)(=W_(ij)) with Equation 9 by using the generated first function F_(ij)and the second function G_(ij). Thereafter, the matrix components m₁₁,m₁₂, m₁₃, m₁₄, . . . , that minimize E_(j) shown in Equation 5 arefigured out in the least square method using this weight W_(j). Then,the weight data generator 23 generates a matrix composed of thecomponents m₁₁, m₁₂, m₁₃, m₁₄, . . . , and then sends the generatedmatrix to the color conversion unit 30.

FIG. 4 is a diagram for explaining the weight determined by the firstfunction F_(ij) and the second function G_(ij) generated by the weightdata generator 23 of the first exemplary embodiment. As shown in FIG. 4,in an area where the color difference distance d between the first colorsignal and the outer boundary of the color gamut is within thepredetermined range, the wider weight W_(ij) is set to be assigned toactual data sets in a wider area as the color difference distance d issmaller, by the first function F_(ij) and the second function G_(ij)generated by the weight data generator 23 of the first exemplaryembodiment. The sum of squares E_(ij) in Equation 5 is calculated withthe weight W_(ij) assigned to the actual data sets (x_(1i), x_(2i),x_(3i), x_(4i)) in the wider area (a shaded area in FIG. 4) than thearea where the conventional weight W_(ij) is assigned to the actual,data sets, the wider area located on the side having smaller colorvalues than that on the outer boundary of the color gamut. Then, theestimated values for the first color signal located around the outerboundary of the color gamut are calculated by performing the local linerregression analysis using the calculated sum of squares E_(j). Thiscalculation allows the estimated values (an estimated point shown inFIG. 4) to have values closer to the real color conversioncharacteristic.

FIG. 5 is a diagram for schematically explaining a relation between thewidth of the weight W_(ij) and the color difference distance d of thefirst color signal to the outer boundary of the color gamut. The “widthof the weight W_(ij)” in FIG. 5 is an example of generation conditionsof the color conversion characteristic, and the generation conditionsare changed according to the color difference distance d. For example,the width of the weight W_(ij) may be defined by use of the colordifference distance d in the color space where the weight W_(ij)determined by the first function F_(ij) and the second function G_(ij)is assigned to the actual data sets in the case of the weight W_(ij)being not less than a predetermined value. For instance, “the width ofthe weight W_(ij)” may be defined as a half width of the maximum weightW_(ij).

As shown in FIG. 5, the width of the weight W_(ij) becomes maximum wherethe color difference distance d is zero (d=0), that is, on the outerboundary of the color gamut, then gradually decreases as the colordifference distance d becomes longer, and is set to a predeterminedwidth where the color difference distance d is not less than d₀ (d≧d₀).The color difference distance d₀ may be set as a color differencedistance d₀ of an area so that a sufficient number of actual data pairs((x_(1i), x_(2i), x_(3i), x_(4i)), (y_(1i), y_(2i), y_(3i))) forobtaining the real color conversion characteristic through calculationis included in the area and the weight W_(ij) is assigned to the actualdata sets in the area under the condition that the weight W_(ij) is setto have the predetermined width.

In this way, by use of the width of the weight W_(ij) that is setaccording to the relation with the color difference distance d as shownin FIG. 5, the actual data pairs located in the wider area (the shadedarea in FIG. 4) around the outer boundary of the color gamut are used tocalculate the sum of squares E_(j) in Equation 5. Consequently, thelocal liner regression analysis with the sum of squares E_(j) isperformed for the first color signal located around the outer boundaryof the color gamut, thereby figuring out the estimated values that arecloser to the real color conversion characteristic.

Here, coefficients for controlling the width of the weight W_(ij) in thefirst function F_(ij) and the second function G_(ij) are the constantsfor normalization (x₁₀, x₂₀, x₃₀, x₄₀), (y₁₀, y₂₀, y₃₀). Accordingly,the weight data generator 23 of the first exemplary embodiment specifiesvariables for normalization (x₁₀(d), x₂₀(d), x₃₀(d), x₄₀(d)), (y₁₀(d),y₂₀(d), y₃₀ (d)) for determining the width of the weight W_(ij)according to the color difference distance d so that the width wouldform, for example, the relation shown in FIG. 5. Then, the weight datagenerator 23 generates the first function F_(ij) and the second functionG_(ij) having the constants for normalization in Equations 6 and 7replaced with the variables for normalization (x₁₀(d), x₂₀ (d), x₃₀ (d),x₄₀ (d)), (y₂₀ (d), y₂₀ (d), y₃₀ (d)).

In other words, the weight data generator 23 of the first exemplaryembodiment generates the following Equations 10 and 11 for changing thewidth of the weight W_(ij) according to the color difference distance dfrom the outer boundary of the color gamut. Then, the weight datagenerator 23 calculates the weight W_(12ij) (=W_(ij)) by substitutingEquations 10 and 11 thus generated into Equation 9. By using this weightW_(ij), the matrix components m₁₁, m₁₂, m₁₃, m₁₄, . . . , that minimizeE_(j) shown in Equation 5 are figured out in the least square method.Thereafter, the weight data generator 23 generates a matrix composed ofthe components m₁₁, m₁₂, m₁₃, m₁₄, . . . , and sends the matrix to thecolor conversion unit 30.

W _(1ij) =F _(ij)(((x _(1i) −x _(1j))/x ₁₀(d))²+((x _(2i) −x _(2j))/x₂₀(d))²+((x _(3i) −x _(3j))/x ₃₀(d))²+((x _(4i) −x _(4j))/x ₄₀(d))²)  (10)

$\begin{matrix}{W_{2{ij}} = {G_{ij}\left( {{\left( {\left( {m_{11}\left( {x_{1i} - x_{1j}} \right)} \right)^{2} + \left( {m_{12}\left( {x_{2i} - x_{2j}} \right)} \right)^{2} + \left( {m_{13}\left( {x_{3i} - x_{3j}} \right)} \right)^{2} + \left( {m_{14}\left( {x_{4i} - x_{4j}} \right)} \right)^{2}} \right)/\left( {y_{10}(d)} \right)^{2}} + {\left( {\left( {m_{21}\left( {x_{1i} - x_{1j}} \right)} \right)^{2} + \left( {m_{22}\left( {x_{2i} - x_{2j}} \right)} \right)^{2} + \left( {m_{23}\left( {x_{3i} - x_{3j}} \right)} \right)^{2} + \left( {m_{24}\left( {x_{4i} - x_{4j}} \right)} \right)^{2}} \right)/\left( {y_{20}(d)} \right)^{2}} + {\left( {\left( {m_{31}\left( {x_{1i} - x_{1j}} \right)} \right)^{2} + \left( {m_{32}\left( {x_{2i} - x_{2j}} \right)} \right)^{2} + \left( {m_{33}\left( {x_{3i} - x_{3j}} \right)} \right)^{2} + \left( {m_{34}\left( {x_{4i} - x_{4j}} \right)} \right)^{2}} \right)/\left( {y_{30}(d)} \right)^{2}}} \right)}} & (11)\end{matrix}$

Note that, as the method for estimating the color conversioncharacteristic in the color processing apparatus 1 of the firstexemplary embodiment, any kind of method for estimating the colorconversion characteristic by use of weighted data pairs may be employedin addition to the above-mentioned method, which is statisticalprocessing, of performing the liner regression analysis using weightedactual data pairs. The employable methods include a method, which isinterpolating processing, of performing interpolation by simplycalculating a weighted average of actual data pairs, a method, which isstatistical processing, using a neural network obtained by learningweighted actual data pairs, and the like.

The forgoing description shows the case where color signals (secondcolor signals) in the L*a*b* color space are estimated from colorsignals (first color signals) in the CMYK color space obtained by theimage data input unit 10, and where colors not included in the actualdata pairs are generated. In the color processing apparatus 1 of thefirst exemplary embodiment, the weight W_(ij) according to the colordifference distance d from the outer boundary of the color gamut is setby the weight data generator 23 also in a case where color signals inthe L*a*b* color space are firstly obtained by the image data input unit10, and where then color signals in the CMYK color space are estimatedfrom the obtained color signals in the L*a*b* color space.

Hereinafter, descriptions will be provided for the setting of the weightW_(ij) according to the color difference distance d from the outerboundary of the color gamut in a case where a color signal in the CMYKcolor space is estimated from a color signal in the L*a*b* color space.Here, presented is a configuration in which the image data input unit 10inputs color signals in the L*a*b* color space, as the first colorsignals in FIG. 1, to the color conversion unit 30, and in which thecolor conversion unit 30 outputs color signals in the CMYK color space,as the second color signals, to the image data output unit 40.

FIG. 6 is a diagram for explaining weight W′_(ij) determined by a firstfunction F_(ij) and a second function G_(ij) for a case where secondcolor signals in the CMYK color space, as output signals, are estimatedfrom first color signals in the L*a*b* color space, as input signals.

In order to estimate the second color signals in the CMYK color spacefrom the first color signals in the L*a*b* color space as shown in FIG.6, Equation 6 might be calculated inversely (an inverse operation mightbe performed) However, since Equation 6 includes the estimation-basevalues of the three-dimensional first color signal (y_(ij), y_(2j),y_(3j)) and the estimated values of the four-dimensional second colorsignal (x_(1j), x_(2j), x_(3j), x_(4j)), Equation 6 has a shortage of aknown value. As a result, Equation 6 may not be uniquely solved throughthe inverse operation. In this case, a part of the second color signal,for example, (x_(4j)) is designated as an estimation-base value, therest of the second color signal, that is, the estimated values, forexample, (x_(1j), x_(2j), x_(3j)) is figured out. To be more precise, ina general method, “K” in the CMYK color space is calculated in the firstplace. For instance, a usable method is to design K coordinates in theCMYK color space corresponding to the color coordinates (L*, a*, b*) inthe L*a*b* color space in advance, or to directly input the colorcoordinates (L*, a*, b*) and the K coordinates as input signals.

Note that, in a case where there is not included processing ofcalculating “K” in the CMYK color space from the color coordinates (L*,a*, b*) in the L*a*b* color space, the second color signal may beestimated through the inverse operation of Equation 6. This is becausethe estimation-base values are the three-dimensional first color signal(L*, a*, b*), and the estimated values are the three-dimensional secondcolor signal (C, M, Y) In this case, the color coordinates (L*, a*, b*,K) are inputted as the first color signal, and the color coordinates (C,M, Y, K) are outputted as the second color signal in FIG. 1.

In this case, the color-gamut distance calculator 21 is not capable ofcalculating the color difference distance d by using the above-mentionedcolor coordinate values (C, M, Y, K) in the CMYK color space. For thisreason, for example, as shown in FIG. 7 (a diagram for explaining thecolor difference distance d in the L*a*b* color space), the outerboundaries of the color gamut in the L*a*b* color space are expressed asa polygon (polyhedron). Then, the distance (color difference distance) dof the first color signal (L*, a*, b*) to the color-gamut outer-boundarypolygon is obtained by calculating the distance to the planeconstituting the color-gamut outer-boundary polygon.

Moreover, as is similar to the above-mentioned case, the weight datagenerator 23 controls the width of the weight W′_(ij) according to thecolor difference distance d of the first color signal to the outerboundary of the color gamut, the distance d obtained from thecolor-gamut distance calculator 21.

In the present case, the weight W′_(ij) is controlled in the L*a*b*color space. For example, as shown in Equation 12, a difference betweeneach pair of corresponding signal components of the first color signal(y_(1j), y_(2j), y_(3j)) of the estimation-base values, and the actualdata sets (y_(1i), y_(2i), y_(3i)) of the first color signal isnormalized. Then, the second weight W′_(2ij) is determined by the secondfunction G_(ij) that is the monotonously decreasing function of theobtained normalized signal with respect to the Euclidean distance. Inaddition, as shown in the following Equation 13, a difference between apair of corresponding signal components, for example, (x_(4j)) (=“K”) ofthe second color signal (x_(1j), x_(2j), x_(3j), x_(3j)) of theestimated values, and the actual data set (x_(4j)) is normalized, andthus the normalized signal is obtained from the difference component ofthe second color signal (“K“). Thereafter, the first weight W′_(1ij) isdetermined by the first function F_(ij) that is the monotonousdecreasing function of the obtained normalized signal with respect tothe Euclidean distance. After that, the two kinds of weight are combinedby a function H shown in Equation 14 to form weight W′_(12ij)(=W′_(ij)). Then, the W′_(12ij) (=W′_(ij)) is used.

W′ _(2ij) =G _(ij)(((y _(1i) −y _(1j))/y ₁₀)²+((y _(2i) −y _(2j))/y₂₀)²+((y _(3i) −y _(3j))/y ₃₀)²)   (12)

W′ _(1ij) =F _(ij)(((x _(4i) −x _(4j))/x ₄₀)²)   (13)

W′ _(12ij) =H(W′ _(1ij) , W′ _(2ij))   (14)

Incidentally, the color-gamut distance calculator 21 may also obtain thecolor difference distance d in the L*a*b* color space by use of a methodnot preparing the color-gamut outer-boundary polygon. For example, whenthe first color signal (L*, a*, b*, K) is inputted, the color conversionunit 30 firstly performs color conversion with the set parameters(weight) and thereby calculates the second color signal (C, M, Y, K).Next, as shown in FIG. 8 (a diagram showing a configuration in which thecolor-gamut distance calculator 21 figures out the color differencedistance d by use of the second color signal calculated by the colorconversion unit 30), the calculated second color signal (C, M, Y, K) istransmitted to the color-gamut distance calculator 21. The color-gamutdistance calculator 21 calculates the color difference distance d by useof the second color signal (C, M, Y, K) obtained from the colorconversion unit 30 in the same manner as the above-mentioned one.According to the newly-calculated color difference d, the weight mayalso be controlled, and the color conversion unit 30 may again convertthe first color signal (L*, a*, b*, K) to the second color signal (C, M,Y, K).

As has been described above, in the color processing apparatus 1 of thefirst exemplary embodiment, when the color conversion characteristic isestimated, the weight (weighting) to be assigned to actual data pairs iscontrolled according to the color difference distance d that is adistance of an input signal (first color signal) as the estimation-basevalues to the outer boundary of the color gamut. This allows theestimated values for the estimation-base values located around the outerboundary of the color gamut to be also accurately calculated, andthereby improves color reproducibility.

Second Exemplary Embodiment

The first exemplary embodiment provides the descriptions for theconfiguration for improving the accuracy of the estimated values for theestimation-base values located around the outer boundary of the colorgamut by adjusting the width of the weight W_(ij). The second exemplaryembodiment provides the descriptions for a configuration for improvingthe accuracy of the estimated values for the estimation-base valueslocated around the outer boundary of the color gamut by shifting thecenter of the weight W_(ij) to the inside of the color gamut.Incidentally, the same reference numerals are used for the samecomponents as those in the first exemplary embodiment, and the detailedexplanations thereof are omitted here.

FIG. 9 is a diagram for explaining the weight W_(ij) determined by afirst function F_(ij) and a second function G_(ij) generated by a weightdata generator 23 of the second exemplary embodiment. As shown in FIG.9, the first function F_(ij) and the second function G_(ij) generated bythe weight data generator 23 of the second exemplary embodiment set theweight W_(ij) for actual data sets in an area inside of the color gamutfarther from the outer boundary of the color gamut as the colordifference distance d is smaller, under the condition that the colordifference distance d between an input signal and the outer boundary ofthe color gamut is not more than the predetermined value in the area.Specifically, the weight data generator 23 generates the first functionF_(ij) and the second function G_(ij) so that, as the color differencedistance d is smaller, the center position of an area is larger shiftedfrom the input signal (estimation-base values) to the inside of thecolor gamut, and the area includes actual data pairs to which the weightW_(ij) is to be assigned. With these functions, as compared with thearea where the conventional weight is assigned to actual data sets, theweight W_(ij) is assigned to actual data sets (x_(1i), x_(2i), x_(3i),x_(4i)) located in an area inside of the color gamut (a shaded area inFIG. 9) farther from the outer boundary of the color gamut, and thus thesum of squares E_(j) in Equation 5 is calculated. Consequently, thelocal liner regression analysis with the sum of squares E_(j) isperformed for the input signal located around the outer boundary of thecolor gamut, thereby figuring out the estimated values (an estimatedpoint shown in FIG. 9) that are closer to the real color conversioncharacteristic.

FIG. 10 is a diagram for schematically explaining a relation between theshift amount of the center of the weight W_(ij) and the color differencedistance d from an input signal (first color signal) to the outerboundary of the color gamut. As shown in FIG. 10, the center of theweight W_(ij) is shifted by the maximum shift amount E where the colordifference distance d is zero (d=0). The shift amount E graduallydecreases as the color difference distance d becomes larger. Then, thecenter of the weight W_(ij) is set not to be shifted (the shiftamount=0) in a range where color difference distance d is not less thand₁ (d≧d₁). The color difference distance d₁ and the maximum shift amountE may be set as a color difference distance d₁ and a maximum shiftamount E of an area so that a sufficient number of actual data pairs((x_(1i), x_(2i), x_(3i), x_(4i)), (y_(1i), y_(2i), y_(3i))) forcalculating the real color conversion characteristic is included in thearea and the weight W_(ij) is assigned to the actual data sets in thearea under the condition that the width of the weight W_(ij) is set to apredetermined value, for example. Here, the shift amount of the centerof the weight W_(ij) is an example of the generation conditions forgenerating the color conversion characteristic that is to be changedaccording to the color difference distance d.

In this way, by use of the weight W_(ij) whose center is shiftedaccording to the relation with the color difference distance d as shownin FIG. 10, actual data pairs located in a wider area (the shaded areain FIG. 9) around the outer boundary of the color gamut are used tocalculate the sum of squares E_(j) in Equation 5. Consequently, thelocal liner regression analysis with the sum of squares E_(j) isperformed for the first color signal located around the outer boundaryof the color gamut, thereby figuring out the estimated values that arecloser to the real color conversion characteristic.

The following Equations 15 and 16 show the first function F_(ij) and thesecond function G_(ij), respectively, that set the center of the weightW_(ij) to be shifted toward the inside of the color gamut according tothe relation in FIG. 10. The weight data generator 23 of the secondexemplary embodiment generates the first function F_(ij) and the secondfunction G_(ij), as shown in Equations 15 and 16, which cause the centerof the weight W_(ij) to be shifted according to the color differencedistance d. Then, the weight data generator 23 calculates the weightW_(12ij) (=W_(ij)) by substituting the generated Equations 15 and 16into Equation 9. By using this weight W_(ij), the matrix components m₁₁,m₁₂, m₁₃, m₁₄, . . . , that minimize E_(j) shown in Equation 5 arefigured out in the least square method. Thereafter, the weight datagenerator 23 generates a matrix composed of the components m₁₁, m₁₂,m₁₃, m₁₄, . . . , and sends the matrix to the color conversion unit 30.

Here, X_(kj)(d) in Equations 15 and 16 is deviated from Equation 17 forsetting, for example, the relation shown in FIG. 10. Incidentally, kdenotes an integer from 1 to 4.

W _(1ij) =F _(ij)(((x _(1i) −x _(1j)(d))/x ₁₀)²+((x _(2i) −x _(2j)(d))/x₂₀)²+((x _(3i) −x _(3j)(d))/x ₃₀)²+((x _(4i) −x _(4j)(d))/x ₄₀)²)   (15)

$\begin{matrix}{w_{2{ij}} = {G_{ij}\left( {{\left( {\left( {m_{11}\left( {x_{1i} - {x_{1j}(d)}} \right)} \right)^{2} + \left( {m_{12}\left( {x_{2i} - {x_{2j}(d)}} \right)} \right)^{2} + \left( {m_{13}\left( {x_{3i} - {x_{3j}(d)}} \right)} \right)^{2} + \left( {m_{14}\left( {x_{4i} - {x_{4j}(d)}} \right)} \right)^{2}} \right)/\left( y_{10} \right)^{2}} + {\left( {\left( {m_{21}\left( {x_{1i} - {x_{1j}(d)}} \right)} \right)^{2} + \left( {m_{22}\left( {x_{2i} - {x_{2j}(d)}} \right)} \right)^{2} + \left( {m_{23}\left( {x_{3i} - {x_{3j}(d)}} \right)} \right)^{2} + \left( {m_{24}\left( {x_{4i} - {x_{4j}(d)}} \right)} \right)^{2}} \right)/\left( y_{20} \right)^{2}} + {\left( {\left( {m_{31}\left( {m_{1i} - {x_{1j}(d)}} \right)} \right)^{2} + \left( {m_{32}\left( {x_{2i} - {x_{2j}(d)}} \right)} \right)^{2} + \left( {m_{33}\left( {x_{3i} - {x_{3j}(d)}} \right)} \right)^{2} + \left( {m_{34}\left( {x_{4i} - {x_{4j}(d)}} \right)} \right)^{2}} \right)/\left( y_{30} \right)^{2}}} \right)}} & (16) \\\left\{ {\begin{matrix}{{0 \leqq d \leqq {d_{1}:{x_{kj}(d)}}} = {x_{kj} - {E\left( {1 - {d/d_{1}}} \right)}}} \\{{d_{1} < {d:{x_{kj}(d)}}} = x_{kj}}\end{matrix}\mspace{20mu} \left( {k = {\left. 1 \right.\sim 4}} \right)} \right. & (17)\end{matrix}$

Moreover, FIG. 11 is a diagram for explaining the weight W_(ij)determined by the first function F_(ij) and the second function G_(ij)of Equations 15 and 16 in a case where second color signals in the CMYKcolor space as output signals are estimated from first color signals inthe L*a*b* color space as input signals. As shown in FIG. 11, as is thecase with the first exemplary embodiment, the second exemplaryembodiment is also capable of estimating the color signals in the CMYKcolor space (second color signal) from the color signals in the L*a*b*color space (first color signal) by setting the weight W_(ij) such thatthe center position of the weight W_(ij) is shifted from the first colorsignal (estimation-base values) toward the inside of the color gamut.

Note that this program may be executed by loading, to a RAM, the programstored in a reserved area such as a hard disk or a DVD-ROM. In addition,another aspect of this program may be executed by a CPU while beingprestored in a ROM. Moreover, when an apparatus is provided with arewritable ROM such as an EEPROM, only this program is sometimesprovided and installed in the ROM after the assembling of the apparatusis completed. In addition, this program may also be transmitted to anapparatus through a network such as the Internet and then installed in aROM included in the apparatus, whereby the program is provided.

The above-mentioned description of the exemplary embodiments of thepresent invention has been provided for the purposes of illustration anddescription. It is not intended to be exhaustive or to limit theinvention to the precise forms disclosed. Obviously, many modificationsand variations will be apparent to practitioners skilled in the art. Theexemplary embodiments were chosen and described in order to best explainbe principles of the invention and its practical applications, therebyenabling others skilled in the art to understand the invention forvarious embodiments and with the various modifications as are suited tothe particular use contemplated. It is intended that the scope of theinvention be defined by the following claims and their equivalents.

1. A color processing apparatus comprising: a first color signalobtaining unit that obtains a first color signal in a first color space;a color conversion unit that converts the first color signal in thefirst color space obtained by the first color signal obtaining unit intoa second color signal in a second color space according to a colorconversion characteristic associating a color signal in the first colorspace with a color signal in the second color space; a calculation unitthat calculates a distance of the first color signal to an outerboundary of a color gamut in the first color space; and a colorconversion characteristic generation unit that generates the colorconversion characteristic to be used by the color conversion unit tomake the conversion, the color conversion characteristic generation unitchanging a generation condition of the color conversion characteristicaccording to the distance of the first color signal calculated by thecalculation unit.
 2. The color processing apparatus according to claim1, wherein the color conversion characteristic generation unit assignsweight to a plurality of color data pairs, the color data pairconsisting of each of a plurality of color data sets in the first colorspace and a corresponding one of a plurality of color data sets obtainedby measuring, in the second color space, a color of an image formed fromeach of the plurality of color data sets in the first color space, thecolor conversion characteristic generation unit generates the colorconversion characteristic according to the plurality of color data pairsto which the weight has been assigned, and changes the weight that isassigned to the plurality of color data pairs according to the distancecalculated by the calculation unit when the color conversioncharacteristic is generated.
 3. The color processing apparatus accordingto claim 2, wherein the color conversion characteristic generation unitchanges the weight to be assigned to the plurality of color data pairslocated around any one of the first color signal and the second colorsignal.
 4. The color processing apparatus according to claim 2, whereinthe color conversion characteristic generation unit sets a wider widthfor an area including the plurality of color data pairs to which theweight is to be assigned, as the distance calculated by the calculationunit is smaller.
 5. The color processing apparatus according to claim 2,wherein the color conversion characteristic generation unit shifts, by ashift amount, a center position of an area including the plurality ofcolor data pairs to which the weight is to be assigned, toward inside ofthe color gamut in the first color space so that the shift amount wouldbecome larger as the distance calculated by the calculation unit issmaller.
 6. The color processing apparatus according to claim 2, whereinthe color conversion characteristic generation unit generates the colorconversion characteristic by performing interpolation processing on theplurality of color data pairs to which the weight has been assigned. 7.The color processing apparatus according to claim 2, wherein the colorconversion characteristic generation unit generates the color conversioncharacteristic by performing statistic processing on the plurality ofcolor data pairs to which the weight has been assigned.
 8. The colorprocessing apparatus according to claim 1, wherein the color conversioncharacteristic generation unit changes the generation condition of thecolor conversion characteristic according to the distance of the firstcolor signal calculated by the calculation unit in a case where thedistance is within a predetermined range.
 9. A color processing methodcomprising: obtaining a first color signal in a first color space;calculating a distance of the obtained first color signal to an outerboundary of a color gamut in the first color space, generating a colorconversion characteristic by using a different generation conditionaccording to the calculated distance of the first color signal, thecolor conversion characteristic associating a color signal in the firstcolor space with a color signal in a second color space; and convertingthe obtained first color signal into a second color signal in the secondcolor space according to the color conversion characteristic.
 10. Thecolor processing method according to claim 9, further comprising:generating the color conversion characteristic according to a pluralityof color data pairs to which a weight has been assigned by changing theweight that is to be assigned to the plurality of color data pairsaccording to the distance, the color data pair consisting of each of aplurality of color data sets in the first color space, and acorresponding one of a plurality of color data sets obtained bymeasuring, in the second color space, a color of an image formed fromeach of the plurality of color data sets in the first color space.
 11. Acomputer readable medium storing a program causing a computer to executea process for color processing, the process comprising: obtaining afirst color signal in a first color space; calculating a distance of theobtained first color signal to an outer boundary of a color gamut in thefirst color space; generating a color conversion characteristic by usinga different generation condition according to the calculated distance ofthe first color signal, the color conversion characteristic associatinga color signal in the first color space with a color signal in a secondcolor space; and converting the obtained first color signal into asecond color signal in the second color space according to the generatedcolor conversion characteristic.
 12. The computer readable mediumstoring a program according to claim 11, wherein, in the process ofgenerating the color conversion characteristic, the color conversioncharacteristic is generated according to a plurality of color data pairsto which a weight has been assigned by changing the weight that is to beassigned to the plurality of color data pairs according to the distance,the color data pair consisting of each of a plurality of color data setsin the first color space and a corresponding one of a plurality of colordata sets obtained by measuring, in the second color space, a color ofan image formed from each of the plurality of color data sets in thefirst color space.
 13. The computer readable medium storing a programaccording to claim 12, wherein, in the process of generating the colorconversion characteristic, the weight to be assigned to the plurality ofcolor data pairs located around the first color signal are changed. 14.The computer readable medium storing a program according to claim 12,wherein, in the process of generating the color conversioncharacteristic, a width of an area including the plurality of color datapairs to which the weight is assigned is set to be wider, as thecalculated distance is smaller.
 15. The computer readable medium storinga program according to claim 12, wherein, in the process of generatingthe color conversion characteristic, a center position of an areaincluding the plurality of color data pairs to which the weight is to beassigned is shifted, by a shift amount, toward inside of the color gamutin the first color space so that the shift amount would become larger asthe calculated distance is smaller.
 16. The computer readable mediumstoring a program according to claim 12, wherein, in the process ofgenerating the color conversion characteristic, the generation conditionof the color conversion characteristic is changed according to thedistance in a case where the distance of the calculated first colorsignal is within a predetermined range.